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Bulletin de la SMF - Titles - 141 (2013) 197-223

Titles < 141

A Riemann-Roch Theorem for dg Algebras
François Petit
Bulletin de la SMF 141, fascicule 2 (2013), 197-223

Télécharger cet article : Fichier PDF

Résumé :
Un théorème de Riemann-Roch pour les dg algèbres
Étant donnée une dg algèbre A, propre et lisse, un dg A-module parfait M et un endomorphisme f de M, nous définissons la classe de Hochschild de la paire (M,f). Cette classe est à valeurs dans l'homologie de Hochschild de l'algèbre A. Notre principal résultat est une formule de type Riemann-Roch faisant intervenir la convolution de deux de ces classes de Hochschild.

Mots-clefs : algèbre différentielle graduée, module parfait, dualité de Serre, homologie de Hochschild, classes de Hochschild, Théorème de Riemann-Roch

Abstract:
Given a smooth proper dg algebra A, a perfect dg A-module M and an endomorphism f of M, we define the Hochschild class of the pair (M,f) with values in the Hochschild homology of the algebra A. Our main result is a Riemann-Roch type formula involving the convolution of two such Hochschild classes.

Keywords: differential graded algebra, perfect module, Serre duality, Hochschild homology, Hochschild class, Riemann-Roch Theorem

Class. math. : 14C40, 16E40, 16E45


ISSN : 0037-9484
Publié avec le concours de : Centre National de la Recherche Scientifique

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